The Mishna says that one is not forgiven for the damage he has caused until he asks forgiveness from the one he caused damage to. This is proven from the passuk that states that Hashem commanded Avimelech to return Sarah to Avraham.
The question is, we don’t seem to see anywhere in the verse that Hashem is telling Avimelech to ask for forgiveness, nor does it say that he asked for Avraham to pardon him, so what’s the proof?
ונ”ל בע”ה that Hashem tells Avimelech to return Sarah to Avraham, and then says that Avraham will daven for Avimelech. The only way that Avraham would daven for him would be if Avraham feels positively toward him. Normally, when one causes an ill effect to his comrade, the compensation for the bad deed is not enough to placate him. Only once the person who has wronged his friend acknowledges his misdeed will the relationship return to its previous state. Thus the implication is that Avimelech is to get back on good terms with Avraham so they will be at the point where Avraham will daven for him.
This would also seem to be the understanding of the second passuk brought, where Avraham indeed davens for Avimelech. Here again we could ask how this proves that Avraham forgave Avimelech and therefore proves that one who has been damaged would also have an obligation to forgive the one who caused the damage? The answer be’H would be as we said, that from the fact that we see that Avraham davened, and he did so in such a way that indeed his tefilos were answered, this shows that he prayed in a fashion that was absolutely sincere and complete. This would only be possible if Avraham had completely forgiven Avimelech for his wrongdoing.